Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic
Probability
2025-09-03 v3
Abstract
We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an exponential distribution, corresponding to the Brownian approximation of a single station queue. The ``single station'' can be constructed precisely and its parameters have a good intuitive interpretation.
Keywords
Cite
@article{arxiv.2304.01499,
title = {Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic},
author = {J. G. Dai and Peter Glynn and Yaosheng Xu},
journal= {arXiv preprint arXiv:2304.01499},
year = {2025}
}